question_answer

A vertical spring with force constant k is fixed on a table A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring, so that the spring is compressed by a distance d. The net work done in the process is

A) \[mg(h+d)+\frac{1}{2}k{{d}^{2}}\]          

B) \[mg(h+d)-\frac{1}{2}k{{d}^{2}}\]

C) \[mg(h-d)-\frac{1}{2}k{{d}^{2}}\]            

D) \[mg(h-d)+\frac{1}{2}k{{d}^{2}}\]

Correct Answer: B

Solution :

Key Idea Work done is equal to  change in energy of body.           Situation is shown in figure. When     mass m falls vertically on spring, then spring is compressed by distance d.                 Hence, net work done in the process is W = Potential energy stored in the spring + Loss of potential energy of mass \[=mg(h+d)-\frac{1}{2}k{{d}^{2}}\]